This invention relates to optoacoustic detectors, commonly referred to as spectrophones, and more particularly to apparatus for measuring the concentrations of absorbing gases in a sample cell using optoacoustic detection of absorption.
A typical optoacoustic absorption detector consists of a single cell for a sample gas with windows through which a chopped radiation beam passes, and means somewhere in communication with the gas in the cell for measuring pressure variations due to absorption of the beam as it is chopped. Present in the signal derived from the pressure measuring means is the desired increase in pressure due to energy absorbed by the sample gas. Superimposed on the desired increase is an unwanted increase due to energy absorbed by the windows causing an increase in temperature of the sample gas, and therefore an increase in pressure of the gas within the cell. This unwanted increase in pressure may be so large as to mask the desired increase in pressure. Minimization of this unwanted increase in pressure is the object of a copending application Ser. No. 599,284 filed July 25, 1975, now Pat. No. 3,995,960 issued Dec. 7, 1976 and the instant application.
As noted in the aforesaid copending application, there is an increasing interest in detecting trace amounts (approaching 0.01 parts per billion) of atmospheric pollutant gases in an air sample. To minimize the unwanted increase in pressure due to energy absorbed by the windows, a transverse path was created in a single cell optoacoustic detector to substantially cancel the effects of the unwanted window absorption by running the beams through a cross-path having windows that were duplicates of the main path windows. The carrier gas is put in first and the background pressure signal adjusted to as near zero as possible by changing the intensity of one or the other of the beams. When a mixture of carrier gas and sample gas is introduced into the detector, the signal produced will automatically be corrected for the background signal effects, and is a measure of the absorption coefficient of the sample gas.
A prior optoacoustic detector developed by Terrence F. Deaton, David A. Depatie and Thomas W. Walker, was disclosed in a paper titled "Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths," Applied Physics Letters, Vol. 26, No. 6, 300-303 (1975). Two identical cells were used in tandem with a differential capacitance monometer between them. Both cells were first filled with non-absorbing gas, and the pressure differential between the cells was then minimized while the laser beam was transmitted through both cells in order to "zero" the instrument. Absorption measurements were then made by replacing the carrier gas in one cell with a mixture of the carrier gas and a sample gas. The pressure differential between the two cells represents the absorption coefficient of the sample gas. Residual pressures which are present as background signals due to absorption by the windows of the cell are effectively balanced out by this double cell arrangement.
The problem with the tandem cell arrangement is that extreme care must be exercised in filling both cells to the same pressure during both the zeroing procedure and the measuring procedure. A micrometer driven piston was placed in each cell to change the cell volume for exact pressure balance. The background noise was reportedly reduced to an equivalent coefficient of 3.3 .times. 10.sup.-7 m.sup.-1 /W of laser power, which is a factor of 100 times better than what was obtainable with a single cell optoacoustic detector. The problem was that the differential monometer had to be mounted to the side of the tandem cells with unnecessarily long connecting pipes.
Another problem was that due to laser beam expansion, more of the volume in the second cell was radiated than in the first cell. Although the same flux of radiation was passing through both cells in tandem, the response of the second cell was necessarily different from the first due to the different illumination volume, making the problem of adjusting for true differential operation very difficult.
A detailed analysis of the magnitude of the pressure signal expected in an optoacoustic detector has been presented by Lars-Goran Rosengren in a paper entitled "Optimal Optoacoustic Detector Design", which appeared in the August, 1975 issue of Applied Optics, Vol. 14, page 1960. His Equation (1) below is an expression for P(.omega.), the rms value of the first harmonic of the pressure in the detector, when the incident optical radiation is chopped at a frequency .omega.. Assuming a square-wave moldulation and a weakly absorbing gas, this expression becomes ##EQU1## where .beta. .ident. 3(.gamma. - 1)/2, and .gamma. is the ratio of the heat capacity of the gas at constant pressure C.sub.p and constant volume C.sub.V ; U is the optical power passing through the detector; .sigma. is the absoprtion cross section of the gas at the laser wavelength illuminating the detector; N is the density of absorbing gas molecules; l is the optical path length through the detector; Q(.omega.) is the acoustical quality of the detector as experienced by the pressure transducer; .tau..sub.t is the thermal relaxation time of the optoacoustic detector; V is the detector volume; .tau..sub.c is the molecular collisional relaxation time; and .tau..sub.4 is the radiative relaxation time.
Assuming that .tau..sub.c &lt;&lt;.tau..sub.r, that .omega..tau..sub.c &lt;&lt;1, that the detector has a cylindrical shape of diameter D and length l, that the detector is filled with a gas that is for the most part diatomic (air), and that the detector chamber is not acoustically resonant Equation (1 ) then becomes simplified to ##EQU2## since .beta. = 0.6 for a diatomic gas.
This equation shows that the detector response varies inversely as the square of the chamber diameter, and that the response will be reduced if the chopping frequency is above the thermal cutoff frequency .omega. = 1/.tau..sub. t. The number density of absorbing molecules, N, applies only to those molecules actually illuminated by the beam of incident radiation, and the chamber diameter, D, applies to the entire detector volume, including any ancillary volume not illuminated. In order for optimum operation of the optoacoustic detector, it is therefore necessary to minimize the detector diameter, and arrange for as much of the volume as possible to be illuminated by the incident radiation. Furthermore, the chopping frequency should be lower than the thermal cutoff frequency.